Here is a right-angled triangular tile. A shape is made using four of these triangular tiles and three square tiles. Work out the perimeter of the shape.
triangle:
I
3cm I
I________
4cm
hypotenuse = 5cm
unfortunately i cant attach images, please help if you can.
"I
3cm I
I________
4cm"
^^ it was meant to resemble a triangle, but the spaces didnt show up :/ just take it as side a = 3cm, b = 4cm, hypotenuse = 5.
imao thats not my priority rn
two such triangles make a 3x4 rectangle
so four of them will make a 6x4 or a 3x8 rectangle
There are many ways to attach the three square tiles, depending on their size
To determine the perimeter of the shape made up of the triangular and square tiles, we need to calculate the lengths of all the sides and then add them together.
Let's begin by finding the lengths of the sides of the triangle using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given:
Hypotenuse = 5 cm
One side of the triangle = 3 cm
Using the Pythagorean theorem, we can solve for the length of the other side:
a^2 + b^2 = c^2
3^2 + b^2 = 5^2
9 + b^2 = 25
b^2 = 25 - 9
b^2 = 16
Taking the square root of both sides, we find:
b = √16
b = 4 cm
So, the lengths of the sides of the triangle are:
Side 1: 3 cm
Side 2: 4 cm
Hypotenuse: 5 cm
Now, let's consider the square tiles. Since all sides of a square are equal, we know that each square tile has sides of equal length. However, we are not given the length of the square sides in the problem. To continue, we need to know the length of one side of the square tiles.
Once we have the length of the square sides, we can calculate the total perimeter by adding up all the side lengths: the three sides of the triangle and the sides of the square tiles.
If you provide the length of the square sides, I can help you calculate the perimeter of the shape.